The United States men’s national team surrounds John Brooks after he scored the game-winning goal to defeat Ghana 2-1.

Julio Cortez / AP

The United States may or may not have played the better football in Monday’s match against Ghana. But it came away with three huge points. That, coupled with Germany’s 4-0 thrashing of Portugal, makes the U.S. slight favorites to advance to the knockout stage. FiveThirtyEight’s World Cup predictions now give the United States a 63 percent chance of advancing, up from 33 percent on Monday morning.

This forecast is based on simulating the rest of the group stage 10,000 times, using estimates of team strength from ESPN’s Soccer Power Index (see here for a lot more methodological detail). It helps to have a computer to do this work when there are so many permutations to consider.

There are nine remaining scenarios involving the Americans’ results, among them possibly beating, losing to or drawing with Portugal, and then the same possibilities against Germany. Some of these are relatively easy to resolve, but others are more complex and depend on the outcomes of the other remaining matches in Group G — Germany against Ghana and Portugal against Ghana — and possibly FIFA’s tie-breaking procedures.

FIFA’s first tiebreaker is based on goal differential. That greatly advantages Germany, with its +4 so far, and greatly harms Portugal, with its -4. The next tiebreaker is based on goals scored (for that reason, it was slightly better for the U.S. to beat Ghana 2-1 than by the 1-0 scoreline that held for most of the game). Finally, head-to-head results are considered — so if it comes down to the U.S. and Ghana and they’re tied on both goals scored and allowed, the U.S. would go in ahead.

Lose twice, and almost certainly go out (there’s one highly unlikely mathematical exception).

Draw once and lose once, and it gets complicated. It’s considerably better for the U.S. to draw against Portugal and lose to Germany than the other way around.

Now here’s the long version:

Beat Portugal, beat Germany: U.S. is in. This rather optimistic scenario is easy to figure. You win all your matches, you win your group.

Beat Portugal, draw Germany: U.S. is in. This scenario guarantees advancement and a tie for first place in the group. If Germany also beats Ghana, however, the U.S. would likely lose the tiebreaker and finish with the second qualifying position.

Beat Portugal, lose to Germany: U.S. is in unless it gets really unlucky. This scenario generally leads to a second-place finish in the group. The exception would be if Ghana beat both Portugal and Germany. In that case, Germany, Ghana and the U.S. would finish in a three-way tie atop the group. One team — probably not Germany and possibly the U.S. — would be the odd one out based on goal differential.

Draw Portugal, beat Germany: U.S. is in. This scenario delivers seven points and guarantees the U.S. first place in the group.

Draw Portugal, draw Germany: U.S. is in. Two draws will be good enough. There won’t be enough points to go around the rest of the group to prevent the U.S. from advancing, though it would probably do so as the second-place team — either because the U.S. finishes second outright or because it loses the tiebreaker to Germany.

Draw Portugal, lose to Germany: U.S. is favored to advance but not safe. This is among the more likely outcomes, so we’ll break it down in more detail. There are a number of permutations based on the results of Ghana’s games against Germany and Portugal.

Under three permutations — Ghana draws with Portugal and either draws with or loses to Germany, or Ghana beats Portugal and loses to Germany, the U.S. will have sole possession of second place and advance.

But under another permutation, the U.S. would be out despite its four points. This case happens if Ghana beats Portugal and Germany, giving both Ghana and Germany six points.

In the other permutations, the U.S. would finish in a tie for second place, with Germany winning the group. If the tie is with Portugal, the U.S. would likely advance on the basis of goal differential. If the tie is with Ghana, it’s a little harder to say.

Lose to Portugal, beat Germany: U.S. is almost certainly in. The only exception is if, in addition to these results, both Germany and Portugal beat Ghana. In that case, the U.S., Germany and Portugal would be tied atop the group with six points. The U.S. would likely get the second position based on goal differential, however, so this scenario is quite safe.

Lose to Portugal, draw Germany: U.S. is a slight underdog to advance. This case is inferior to losing to Germany and drawing with Portugal because it gives Portugal three points and makes it much more of a threat to advance. The permutations get complicated:

The U.S. is almost certainly out in the cases where Portugal beats Ghana. That, coupled with a Portuguese win against the U.S., would give Portugal six points and it would leapfrog the U.S. in the standings. (The only exception is if Germany gets blown out by Ghana so badly that it loses the tiebreaker to the U.S. — not at all likely.)

Only one permutation guarantees the U.S. entry: if Germany beats Ghana but Ghana beats Portugal.

A number of other permutations involve ties for second place, sometimes against Germany (bad for the U.S.) and sometimes against Portugal (good for the U.S.).

Finally, there could even be a four-way tie for first if Ghana draws with Portugal and beats Germany!

Lose to Portugal, lose to Germany: U.S. is mathematically alive but needs a miracle. This almost certainly dooms the United States. But just as there’s a wild-card scenario in which it could win twice but fail to advance, there’s one in which it could lose both remaining matches but move on. That would happen if Ghana beats Portugal and loses to Germany. Then Germany would win the group with nine points, and the U.S. would be in a three-way tie for second with Portugal and Ghana. The U.S. would need to beat both teams on the tiebreaker. It wouldn’t be how you script these things, but neither was Monday’s win.

One final note: The Americans’ chances to advance should improve slightly when we rerun the numbers on Tuesday morning, as they’ll reflect the change in the Soccer Power Index, which we update overnight. It’s not that the United States’ SPI will increase so much as that Portugal’s will decline: Portugal looks much more beatable (or at least drawable) after its 4-0 defeat. SPI is not sophisticated enough to account for the red card to Portugal’s Pepe (who will miss the match against the U.S.) or the injury to the U.S.’s Jozy Altidore — nor for the fact that the Americans’ quality of play on Monday was not as impressive as the scoreline.

Sign up for our newsletters to keep up with our favorite articles, charts and regressions.
We have three on offer: a curated digest of the best of FiveThirtyEight from the past week; Ctrl + ←, our weekly look at the best data journalism from around the web; and Significant Digits, our roundup of numbers in the news.
Enter your email below, and we’ll be in touch.